The data in Table 5.4 is taken from Feigl and Zelen [5]. The white blood cell counts for patients who died of acute myelogenous leukemia and their survival times were recorded. They were classified as AG positive or AG negative according to the absence or presence of a certain characteristic of white blood cells.
Feigl and Zelen's Leukemia Data AG Positive
AG Negative White Blood Survival Time White Blood Survival Time Count (WBC) (in weeks) Count (WBC) (in weeks) 2300 65 4400 56 750 156 3000 65 4300 100 4000 17 2600 134 1500 7 6000 16 9000 16 10500 108 5300 22 10000 121 10000 3 17000 4 19000 4 5400 39 27000 2 7000 143 28000 3 9400 56 31000 8 32000 26 26000 4 35000 22 21000 3 100000 1 79000 30 100000 1 100000 4 52000 5 100000 43 100000 65 Feigl and Zelen's Leukemia Data
The data is analysed to determine if survival times can be predicted. The data can be loaded from the file leuk.mat in the data folder (using the MATLAB load command), or the LOAD Data File menu item.
>> who Your variables are: Ag Time Wbc
The variable Ag contains 1 if the patient is AG positive, and a 0 if AG negative; Wbc is the white blood cell count; Time is the survival time. The exponential distribution and reciprocal link function are used (though the original paper uses the identity link function). The exponential distribution is equivalent to the gamma distribution with the scale parameter set to 1. The first step is to alter the error distribution by selecting the Distribution menu item in the main glmlab window, and choosing the gamma distribution. The scale parameter is then altered by clicking on the Scale Parameter menu item in the main glmlab window, and selecting Fixed Value. A new window appears; enter in the fixed value of the scale parameter (in this case, 1); see Figure 5.4. This has effectively selected the exponential distribution.
Entering a Fixed Value for the Scale Parameter
The original paper analyses the logarithm of the white blood cell counts, with the survival time, the AG factor, plus their interaction as covariates. The complete model can be fitted by typing in the variables in the main glmlab window as shown in Figure 5.4. Note the use of the fac command (because Ag is qualitative) and the @ symbol.
Pressing the FIT MODEL button produces the following estimates:
Variables Entered for Example 5.4
------------------------------------------------------------
Estimate S.E. Variable
------------------------------------------------------------
8.478205 1.655453 Constant
-0.481829 0.173635 log(Wbc)
-4.137813 2.570290 Ag(2)
0.328110 0.266888 log(Wbc)@Ag(2)
------------------------------------------------------------
Scaled Deviance: 38.554607 (change: +0.000000)
Residual df: 29 (change: +0)
Scale parameter (dispersion parameter): 1.000000